Pulley Speed and Ratio Calculator

How is speed worked out from pulley size?

A belt travels at the same speed around both pulleys, so their rim speeds are equal and the rotational speeds are inversely proportional to the diameters: n₁ × d₁ = n₂ × d₂. The driven speed is therefore n₂ = n₁ × d₁ / d₂. The large pulley turns slowly, the small one fast.

The speed ratio is i = n₁ / n₂ = d₂ / d₁. A ratio above 1 reduces speed and raises torque by the same factor.

Slip

Flat and V belts creep slightly on the pulleys under load, so the real driven speed is a little below the calculated one. With slip s the relation becomes n₂ = n₁ × (d₁ / d₂) × (1 − s). Timing belts do not slip and their ratio is fixed exactly by the tooth counts.

Belt speed

The linear speed of the belt is v = π × d₁ × n₁, with speed in revolutions per second. Manufacturer catalogues give the power rating of a belt as a function of this speed.

Example

A 1450 rpm motor carries a 100 mm pulley and the machine shaft a 300 mm pulley. The driven speed is 1450 × 100 / 300 = 483 rpm and the ratio is 3. Belt speed is π × 0.1 × 1450 / 60 = 7.6 m/s. With 2 percent slip the driven speed drops to 474 rpm.

Limits

This tool covers only the relation between speed and diameter. The power a belt can carry, the number of belts needed and the smallest permitted pulley diameter depend on the belt section and come from the manufacturer's catalogue.